Contenido del curso

Evaluación

Recursos

Clases

Lunes, Martes, Jueves y Viernes 11:00 – 13:00 Sala 504

Sala de teams

Software

Interpretes: Python, R, Latex(TEXLive), Anaconda.

IDE: Visual Studio Code, Google Colaboratory (R, Python)

Librerías Pandas, Matplotlib, Seaborn, Keras, Tensorflow, Numpy, SciKit-Learn, SciPy

Seguimiento de Aprendizaje: Moodle

A little reminder …

A little reminder …

A little reminder …

A little reminder …

A little reminder …

Exploratory Data Analysis (EDA)

Definition

The art of looking the underlying structure of the information through one or more datasets.

Definition by Diaconis, P.

We look at numbers or graphs and try to find patterns. We pursue leads suggested by background information, imagination, patterns perceived, and experience with other data analyses.

Exploratory Data Analysis (EDA)

EDA, depends on two things:

1. Type of variable scale (information type, categorical, numerical, continuous, discrete, etc).

2. Objective and type of the analysis (graphical, numerical, correlation, etc)

Learning from the example

Spotify

“Spotify offers digital copyright restricted recorded music and podcasts, including more than 82 million songs, from record labels and media companies” from wikipedia

Spotify Dataset

The data set is located in the kaggle site. Dataset

Learning from the example

Analysis Objective

Spotify wants to know if there is a relationship between the popularity of a song and the number of followers of its singers. The above to generate strategies to attract new singers to the platform.

Learning from the examples

General Workflow

1. Import dataset.
2. Preprocessing dataset.
3. EDA on the datasets.
4. Train the machine learning model.
5. Predict the target using the trained model.

Preprocessing dataset.

General workflow for Preprocessing

1. Check the digital structure of the dataset
2. Check for digital information type
3. Check for nan
4. Check for outlier

Preprocessing dataset.

type(data_spotify)

pandas.core.frame.DataFrame

data_spotify.shape

(586671, 20)

data_spotify.size

11733420

Linear Regression, python preparation

import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
import numpy as np
archivoData = path_to_data+"/Salario/data_for_class.csv"
data = pd.read_csv(archivoData,delimiter=",", decimal=".")

Salary vs Years of experience scatter plot

ax1 = sns.scatterplot(data=data, x="YearsExperience", y="Salary")
ax1.set(xlabel='x = YearsExperience', ylabel='y = Salary')
plt.show()

Salary vs Years of experience scatter plot

Salary histogram

ax2 = sns.displot(data=data, x="Salary")
plt.show()

Salary histogram

Linear Regression

Linear Regression

In the example, in previous slide, data was modelled as a linear function. The difference (error) between the modelled data \(\left( \hat{y}_n \right)\) and actual data \(\left( y_n \right)\) can be written as

Some other examples of cost function

\[E = \sqrt{\frac{1}{N} \sum_{n=1}^{N}{\left( \hat{y}_n - y_n \right)^2}}\]

\[E = \frac{1}{N} \sum_{n=1}^{N}{\left| \hat{y}_n - y_n \right| }\]

Gradient Descent algorithm

Looking the cost surface, we notices that this surface has a global minimum. If we could have an algorithm which automatically finds it.

Cost Surface

Gradient Descent algorithm

Indeed, there are multiples algorithms for minima searching. The most famous is the one named as least squares but in this course we will use the gradient descent algorithm.

Assuming that the data model is a function \(f\left(\theta_i, x_n, y_n\right)\), where \(\theta\) is known as model parameter.

Gradient Descent algorithm

\[\boldsymbol{\theta}_i = \left[ \theta_1, \theta_0 \right]^T\]

\[\hat{y}_n = \theta_1 x_n + \theta_0\]

\[E = \frac{1}{N} \sum_{n=1}^{N}{\left( \theta_1 x_n + \theta_0 - y_n \right)^2}\]

Gradient Descent algorithm

Gradient Descent algorithm

Changing the cost function and the data model

\[ \begin{eqnarray} E & = & \frac{1}{N} \sqrt{u}\\ \frac{\partial E}{\partial \boldsymbol{\theta}_{0}} &=& \frac{1}{2 N \sqrt{u}} \frac{\partial u}{\partial \boldsymbol{\theta}_{0}}\\ \frac{\partial u}{\partial \boldsymbol{\theta}_{0}} &=& 2\sum_{n=1}^{N}{\left( \theta_2 x_{n}^{2} + \theta_1 x_n + \theta_0 - y_n \right)}\\ \frac{\partial E}{\partial \boldsymbol{\theta}_{0}} &=& \frac{2\sum_{n=1}^{N}{\left( \theta_2 x_{n}^{2} + \theta_1 x_n + \theta_0 - y_n \right)}}{2 N \sqrt{u}} \end{eqnarray} \]

Changing the cost function and the data model

\[ \begin{eqnarray} \frac{\partial E}{\partial \boldsymbol{\theta}_{0}} &=& \frac{\sum_{n=1}^{N}{\left( \theta_2 x_{n}^{2} + \theta_1 x_n + \theta_0 - y_n \right)}}{N \sqrt{\sum_{n=1}^{N}{\left( \theta_2 x_{n}^{2} + \theta_1 x_n + \theta_0 - y_n \right)^2}}}\\ \frac{\partial E}{\partial \boldsymbol{\theta}_{1}} &=& \frac{\sum_{n=1}^{N}{x_n \left( \theta_2 x_{n}^{2} + \theta_1 x_n + \theta_0 - y_n \right)}}{N \sqrt{\sum_{n=1}^{N}{\left( \theta_2 x_{n}^{2} + \theta_1 x_n + \theta_0 - y_n \right)^2}}}\\ \frac{\partial E}{\partial \boldsymbol{\theta}_{2}} &=& \frac{\sum_{n=1}^{N}{x_n^2 \left( \theta_2 x_{n}^{2} + \theta_1 x_n + \theta_0 - y_n \right)}}{N \sqrt{\sum_{n=1}^{N}{\left( \theta_2 x_{n}^{2} + \theta_1 x_n + \theta_0 - y_n \right)^2}}} \end{eqnarray} \]